On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.     

Permutations with small maximal k-consecutive sums

Let $n$ and $k$ be positive integers with $n>k$. Given a permutation $({\pi }_1,\dots ,{\pi }_n)$ of integers $1,\dots ,n$, we consider $k$-consecutive sums of $\pi$, i.e., $s_i?{\sum }_{j=0}^{k?1}{\pi }_{i+j}$ for $i=1,\dots ,n$, where we let ${\pi }_{n+j}={\pi }_j$. What we want to do in this paper is to know the exact value of $\mathsf{msum}(n,k)?min\left\{max\{s_i:i=1,\dots ,n\}?\frac{k(n+1)}{2}:\pi \in S_n\right\},$ where $S_n$ denotes the set of all permutations of $1,\dots ,n$. In this paper, we determine the exact values of $\mathsf{msum}(n,k)$ for some particular cases of $n$ and $k$. As a corollary of the results, we obtain $\mathsf{msum}(n,3)$, $\mathsf{msum}(n,4)$ and $\mathsf{msum}(n,6)$ for any $n$.     

Electrodeposition of Silver Vanadate Films: A Tale of Two Polymorphs

Two polymorphs of AgVO₃, namely the α- and β- forms, were prepared and their physical, structural, optical, electrochemical, and photoelectrochemical characteristics were compared using a battery of experimental and theoretical tools. A two-step method, previously developed in the our laboratory for the electrodeposition of inorganic semiconductor films, was applied to the electrosynthesis of silver vanadate (AgVO₃) films on transparent, conducting oxide surfaces. In the first step, silver was cathodically deposited from a non-aqueous bath containing silver nitrate. In the second step, the silver film was anodically stripped in an aqueous medium containing ammonium metavanadate. The anodically generated silver ions at the interface underwent a precipitation reaction with the vanadate species to generate the desired product in situ. Each of these steps were mechanistically corroborated via the use of electrochemical quartz crystal microgravimetry, used in conjunction with voltammetry and coulometry. As-deposited films were crystalline and showed p-type semiconductor behavior. Theoretical insights are provided for the electronic origin of the α→β phase transformation in AgVO₃ and the disparate optical band gaps of the two polymorphs. Finally, implications for the application of this material in solar cells are provided.     

Synthesis and crystal structures of phenylalanine ester-introduced palladium(II) and platinum(II) complexes and their cytotoxicities

Research on Chemical Intermediates - Phenylalanine ester-introduced palladium(II) and platinum(II) complexes were synthesized. Taking advantage of the formation of Schiff bases by amino acids as an...     

Weak Antiferromagnetic Exchange and Ferromagnetic Alignment of FeII (S=2) Spins in Differently Charged {HAT ⋅ (FeIICl2)3}n (n=2- and 3-) Assemblies of Hexaazatriphenylenes (HAT)

Hexaazatrianthracene (HATA) and hexaazatriphenylenehexacarbonitrile {HAT(CN)₆} are reduced by metallic iron in the presence of crystal violet (CV⁺)(Cl⁻). Anionic ligands are produced, which simultaneously coordinate three Fe^IICl₂ to form (CV⁺)₂{HATA ⋅ (Fe^IICl₂)₃}²⁻ ⋅ 3 C₆H₄Cl₂ ( 1 ) and (CV⁺)₃{HAT(CN)_6. (Fe^IICl₂)₃}³⁻ ⋅ 0.5CVCl ⋅ 2.5 C₆H₄Cl₂ ( 2 ). High-spin (S=2) Fe^II atoms in both structures are arranged in equilateral triangles at a distance of 7 Å. An antiferromagnetic exchange is observed between Fe^II in {HATA ⋅ (Fe^IICl₂)₃}²⁻ ( 1 ) with a Weiss temperature (Θ) of −80 K, the PHI estimated exchange interaction (J) is −4.7 cm⁻¹. The {HAT(CN)₆ ⋅ (Fe^IICl₂)₃}³⁻ assembly is obtained in 2 . The formation of HAT(CN)₆^.3− is supported by the appearance of an intense EPR signal with g=2.0037. The magnetic behavior of 2 is described by a strong antiferromagnetic coupling between the Fe^II and HAT(CN)₆^.3− spins with J₁=−164 cm⁻¹ (−2 J formalism) and by a weaker antiferromagnetic coupling between the Fe^II spins with J₂=−15.4 cm⁻¹. The stronger coupling results in the spins of the three Fe^IICl₂ units to be aligned parallel to each other in the assembly. As a result, an increase of the χ_MT values is observed with the decrease of temperature from 9.82 at 300 K up to 15.06 emu ⋅ K/mol at 6 K, and the Weiss temperature is also positive being at +23 K. Thus, a change in the charge and spin state of the HAT-type ligand to ⋅3⁻ results in ferromagnetic alignment of the Fe^II spins, yielding a high-spin (S=11/2) system. DFT calculations showed that, due to the high symmetry and nearly degenerated LUMO of both HATA and HAT(CN)₆, their complexes with Fe^IICl₂ have a variety of closely lying excited high-spin states with multiplicity up to S=15/2.     

One-step synthesis of (1-iodovinyl) arenes from trimethylsilyl ethynylarene through iodotrimethylsilane-mediated hydroiodation

One-step access to (1-iodovinyl) arenes from trimethylsilyl ethynylarenes is described. The method is superior to a conventional multi-step approach, and is enhanced by the Sonogashira reaction that provides ready access to a variety of trimethylsilyl ethynylarenes.